Finding the Terms and Proving Induction for a Numerical Sequence

[snaidu228]

Homework Statement

If x is a real number, we define [x] as being the largest integer <= x. For example, [1.2] = 1,
[-1.1] = -2, [1] = 1, [11/3]3 = 3, . . .
Let {an}n>=1 be the numerical sequence defined by:
a1 = 3; and an = a[n/2], for n>=2

(a) Give the terms a1; a2; ... ; a8 of this sequence.
(b) Prove that an = 3; For all n>=  1

Homework Equations

The Attempt at a Solution

I'm not sure what induction has to do with this... I don't really get it.

 

[Mark44]

Homework Statement

If x is a real number, we define [x] as being the largest integer <= x. For example, [1.2] = 1,
[-1.1] = -2, [1] = 1, [11/3]3 = 3, . . .
Let {an}n>=1 be the numerical sequence defined by:
a1 = 3; and an = a[n/2], for n>=2

(a) Give the terms a1; a2; ... ; a8 of this sequence.
(b) Prove that an = 3; For all n>=  1

Homework Equations

The Attempt at a Solution

I'm not sure what induction has to do with this... I don't really get it.

Write out a few terms of the sequence to get a feel for what it's doing.
a₁ = 3, a₂ = ?, a₃ = ?, a₄ = ? And so on, through a₈. That's part a.